Eigenvalue problems in anisotropic Orlicz–Sobolev spaces

Mihai Mihăilescu; Gheorghe Moroşanu; Vicenţiu Rădulescu

doi:10.1016/j.crma.2009.02.023

Partial Differential Equations

Eigenvalue problems in anisotropic Orlicz–Sobolev spaces
[Problèmes de valeurs propres dans les espaces d'Orlicz–Sobolev anisotropes]

Présenté par : Philippe G. Ciarlet

Mihai Mihăilescu ^1,² ; Gheorghe Moroşanu ² ; Vicenţiu Rădulescu ^1,³

¹ University of Craiova, Department of Mathematics, Street A.I. Cuza No. 13, 200585 Craiova, Romania
² Department of Mathematics, Central European University, 1051 Budapest, Hungary
³ Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 014700 Bucharest, Romania

Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 521-526.

Résumé
Abstract

On établit des conditions suffisantes pour l'existence des solutions pour une classe de problèmes non linéaires de valeurs propres avec des opérateurs différentiels non homogènes dans les espaces d'Orlicz–Sobolev.

We establish sufficient conditions for the existence of solutions to a class of nonlinear eigenvalue problems involving nonhomogeneous differential operators in Orlicz–Sobolev spaces.

Reçu le : 2009-01-05
Accepté le : 2009-02-06
Publié le : 2009-03-13

DOI : 10.1016/j.crma.2009.02.023

Affiliations des auteurs :

Mihai Mihăilescu ^{1, 2} ; Gheorghe Moroşanu ² ; Vicenţiu Rădulescu ^{1, 3}

¹ University of Craiova, Department of Mathematics, Street A.I. Cuza No. 13, 200585 Craiova, Romania
² Department of Mathematics, Central European University, 1051 Budapest, Hungary
³ Institute of Mathematics “Simion Stoilow” of the Romanian Academy, 014700 Bucharest, Romania

@article{CRMATH_2009__347_9-10_521_0,
     author = {Mihai Mih\u{a}ilescu and Gheorghe Moro\c{s}anu and Vicen\c{t}iu R\u{a}dulescu},
     title = {Eigenvalue problems in anisotropic {Orlicz{\textendash}Sobolev} spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {521--526},
     publisher = {Elsevier},
     volume = {347},
     number = {9-10},
     year = {2009},
     doi = {10.1016/j.crma.2009.02.023},
     language = {en},
}

TY  - JOUR
AU  - Mihai Mihăilescu
AU  - Gheorghe Moroşanu
AU  - Vicenţiu Rădulescu
TI  - Eigenvalue problems in anisotropic Orlicz–Sobolev spaces
JO  - Comptes Rendus. Mathématique
PY  - 2009
SP  - 521
EP  - 526
VL  - 347
IS  - 9-10
PB  - Elsevier
DO  - 10.1016/j.crma.2009.02.023
LA  - en
ID  - CRMATH_2009__347_9-10_521_0
ER  -

%0 Journal Article
%A Mihai Mihăilescu
%A Gheorghe Moroşanu
%A Vicenţiu Rădulescu
%T Eigenvalue problems in anisotropic Orlicz–Sobolev spaces
%J Comptes Rendus. Mathématique
%D 2009
%P 521-526
%V 347
%N 9-10
%I Elsevier
%R 10.1016/j.crma.2009.02.023
%G en
%F CRMATH_2009__347_9-10_521_0

Mihai Mihăilescu; Gheorghe Moroşanu; Vicenţiu Rădulescu. Eigenvalue problems in anisotropic Orlicz–Sobolev spaces. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 521-526. doi : 10.1016/j.crma.2009.02.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.02.023/

Bibliographie
Cité par

[1] R. Adams Sobolev Spaces, Academic Press, New York, 1975

[2] Ph. Clément; M. García-Huidobro; R. Manásevich; K. Schmitt Mountain pass type solutions for quasilinear elliptic equations, Calc. Var., Volume 11 (2000), pp. 33-62

[3] Ph. Clément; B. de Pagter; G. Sweers; F. de Thélin Existence of solutions to a semilinear elliptic system through Orlicz–Sobolev spaces, Mediterr. J. Math., Volume 1 (2004), pp. 241-267

[4] I. Fragalà; F. Gazzola; B. Kawohl Existence and nonexistence results for anisotropic quasilinear equations, Ann. Inst. H. Poincaré, Analyse Non Linéaire, Volume 21 (2004), pp. 715-734

[5] M. Mihăilescu, G. Moroşanu, V. Rădulescu, Eigenvalue problems for anisotropic elliptic equations: An Orlicz–Sobolev space setting, preprint

[6] M. Mihăilescu; V. Rădulescu Eigenvalue problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces, Analysis and Applications, Volume 6 (2008) no. 1, pp. 1-16

[7] M. Mihăilescu; V. Rădulescu Neumann problems associated to nonhomogeneous differential operators in Orlicz–Sobolev spaces, Ann. Inst. Fourier, Volume 58 (2008) no. 6, pp. 2087-2111

[8] S.M. Nikol'skii On imbedding, continuation and approximation theorems for differentiable functions of several variables, Russian Math. Surv., Volume 16 (1961), pp. 55-104

[9] J. Rákosník Some remarks to anisotropic Sobolev spaces I, Beiträge zur Analysis, Volume 13 (1979), pp. 55-68

[10] J. Rákosník Some remarks to anisotropic Sobolev spaces II, Beiträge zur Analysis, Volume 15 (1981), pp. 127-140

[11] M. Struwe Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer, Heidelberg, 1996

[12] M. Troisi Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche Mat., Volume 18 (1969), pp. 3-24

Cité par Sources :

Commentaires - Politique